Altitude-dependent polarization in radio pulsars

Abstract

Because of the corotation, the polarization angle (PA) curve of a pulsar lags the intensity profile by 4r/Rlc rad in pulse phase. I present a simple and short derivation of this delay-radius relation to show that it is not caused by the aberration (understood as the normal beaming effect) but purely by contribution of corotation to the electron acceleration in the observer's frame. Available altitude-dependent formulae for the PA curve are expressed through observables and emission altitude to make them immediately ready to use in radio data modelling. The analytical approximations for the altitude-dependent PA curve are compared with exact numerical results to show how they perform at large emission altitudes. I also discuss several possible explanations for the opposite-than-normal shift of PA curve, exhibited by the pedestal emission of B1929+10 and B0950+08.Comment: 12 pages, 5 figures, accepted by MNRAS after minor change

Absolute emission altitude of pulsars: PSRs B1839+09, B1916+14, and B2111+46

“…We can think of two viable alternatives in this scenario: either (1) adapt or modify the BCW91 formulation for a variable emission altitude r (Dyks 2008) or (2) fit the BCW91 curve for regions of the PPA profile having a relatively constant value of r. We prefer the latter alternative to evade the modification of the theory behind the BCW91 model. Here we note that α and β are not invoked as fit parameters; instead we used their published values in Eq.…”

Rotational asymmetry of pulsar profiles

“…the aberration (contributing one r / R lc ) and the retardation (contributing another r / R lc ). The symbol φ f denotes the absolute fiducial phase, determined by the detection of a photon emitted from the centre of the NS exactly at the moment when the dipole axis was in the ‐observer plane (see Dyks 2008 for details).…”

“…It is the inflection point of the IOF trajectory that is located at ( r cst , s cst ) [or ( r cst , θ cst )]. Thus, the region of the caustic pile‐up () is simultaneously the region of the zero‐curvature of electron trajectory in IOF, as localized by in Dyks (2008). By noting that one can rewrite in the form For a laterally extended emitter the zero (or minimum) curvature corresponds to the steepest gradient of the polarization angle swing.…”

“…The corotation increases the curvature of electron trajectories on the LS of the MP, whereas it decreases the curvature on the TS (Thomas & Gangadhara 2007; Dyks 2008). The question of how this affects radio emissivity is a complicated one, because it depends on details of the amplification process.…”

“…The IOF acceleration can be expressed as a sum of two vectors where is the CF‐acceleration caused by the curvature of magnetic lines and is the acceleration generated by the corotation (see Dyks 2008 for a simple derivation; note that we still keep the discussion limited to the orthogonal case of α=ζ≃ 90°). The symbol ρ B denotes the radius of curvature of ‐field lines in the CF: where (with a hat) is a unit vector along that radius of curvature and is a unit vector in the direction of the rotational azimuth.…”